Related papers: Entropy under disintegrations
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…
We consider the problem of when a symbolic dynamical system supports a Borel probability measure that is invariant under every element of its automorphism group. It follows readily from a classical result of Parry that the full shift on…
This paper addresses the question of the fluctuations of the empirical entropy of a chain of infinite order. We assume that the chain takes values on a finite alphabet and loses memory exponentially fast. We consider two possible…
According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…
We investigate the asymptotic equipartition property (AEP) in the context of multipartite entanglement measures on pure states. Specifically, we formulate AEP for subadditive entanglement measures that admit certain weak conditions. This is…
Entropic independence is a structural property of measures that underlies modern proofs of functional inequalities, notably (modified) log-Sobolev inequalities, via ``annealing'' or local-to-global schemes. Existing sufficient criteria for…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
In the present work, we provide the asymptotic behavior of the residual-past entropy, of the mean residual-past lifetime distribution and of the residual-past inaccuracy measure. We are interested in these measures of uncertainty in the…
We study the exponential decay of relative entropy functionals for zero-range processes on the complete graph. For the standard model with rates increasing at infinity we prove entropy dissipation estimates, uniformly over the number of…
We establish a general criterion on the upper semi-continuity of partial entropy in all directions for $C^{1+\alpha}$ diffeomorphisms: it holds when the respective sums of Lyapunov exponents are continuous. This addresses, in arbitrary…
Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (one-dimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…